Novel Architecture of Parameterized Quantum Circuit for Graph Convolutional Network

TL;DR

This paper introduces a novel quantum graph convolutional network architecture using parameterized quantum circuits, capable of handling topological data with fewer parameters, and demonstrates comparable performance to classical GCNs in node classification tasks.

Contribution

The paper designs a quantum GCN architecture inspired by classical GCNs, incorporating adjacency matrices and gradient descent on quantum circuits, expanding PQC capabilities for topological data.

Findings

QGCN achieves similar accuracy to classical GCN on Cora dataset.

Using adjacency matrices improves quantum topological data classification.

QGCN requires fewer tunable parameters than classical GCNs.

Abstract

Recently, the implementation of quantum neural networks is based on noisy intermediate-scale quantum (NISQ) devices. Parameterized quantum circuit (PQC) is such the method, and its current design just can handle linear data classification. However, data in the real world often shows a topological structure. In the machine learning field, the classical graph convolutional layer (GCL)-based graph convolutional network (GCN) can well handle the topological data. Inspired by the architecture of a classical GCN, in this paper, to expand the function of the PQC, we design a novel PQC architecture to realize a quantum GCN (QGCN). More specifically, we first implement an adjacent matrix based on linear combination unitary and a weight matrix in a quantum GCL, and then by stacking multiple GCLs, we obtain the QGCN. In addition, we first achieve gradients decent on quantum circuit following the parameter-shift rule for a GCL and then for the QGCN. We evaluate the performance of the QGCN by conducting a node classification task on Cora dataset with topological data. The numerical simulation result shows that QGCN has the same performance as its classical counterpart, the GCN, in contrast, requires less tunable parameters. Compared to a traditional PQC, we also verify that deploying an extra adjacent matrix can significantly improve the classification performance for quantum topological data.